> It didn't take long before a strawman got pulled out of nowhere.

It's not a strawman. It's a central example of what I had in mind when I used the word "axiom".

> if one disagrees with the wild conjectures of the rationalists, which they call "axioms"

They don't refer to wild conjectures as axioms.

> they blame you for rejecting the Pythagorean Theorem or some such.

There is no "blame" going on here. Someone said I sounded like a cult member (which incidentally is insulting and inappropriate on HN; but I thought I would try to steer the discussion back on course) and I correctly explained why that perception is irrelevant. When I said

> The entire point of the exercise is to establish that certain things are true, and that this is not because of faith, and that disbelieving them cannot make them false.

That is, in fact, inarguably true. Bayes' Law is an example of that exact sort of thing. If you don't believe that conditional probabilities can be worked out that way, that won't change the fact that conditional probabilities can in fact be worked out that way; and it won't change the fact that in the long run I will be able to exploit your fallacy in games of chance.

The other poster gave no example of supposedly false or unsound axioms, so I cannot be strawmanning by failing to respond to them. My assertion is that such false or unsound axioms are not, in fact, in play. The burden of proof lies with those claiming their existence.